H2O + SO2 + KI = S + KOH + I2

H_2O water + SO_2 sulfur dioxide + KI potassium iodide ⟶ S mixed sulfur + KOH potassium hydroxide + I_2 iodine

Balance the chemical equation algebraically: H_2O + SO_2 + KI ⟶ S + KOH + I_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 KI ⟶ c_4 S + c_5 KOH + c_6 I_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and K: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 = c_5 S: | c_2 = c_4 I: | c_3 = 2 c_6 K: | c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + SO_2 + 4 KI ⟶ S + 4 KOH + 2 I_2

+ + ⟶ + +

water + sulfur dioxide + potassium iodide ⟶ mixed sulfur + potassium hydroxide + iodine

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + KI ⟶ S + KOH + I_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 2 H_2O + SO_2 + 4 KI ⟶ S + 4 KOH + 2 I_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 2 | -2 SO_2 | 1 | -1 KI | 4 | -4 S | 1 | 1 KOH | 4 | 4 I_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) SO_2 | 1 | -1 | ([SO2])^(-1) KI | 4 | -4 | ([KI])^(-4) S | 1 | 1 | [S] KOH | 4 | 4 | ([KOH])^4 I_2 | 2 | 2 | ([I2])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2O])^(-2) ([SO2])^(-1) ([KI])^(-4) [S] ([KOH])^4 ([I2])^2 = ([S] ([KOH])^4 ([I2])^2)/(([H2O])^2 [SO2] ([KI])^4)

Construct the rate of reaction expression for: H_2O + SO_2 + KI ⟶ S + KOH + I_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 2 H_2O + SO_2 + 4 KI ⟶ S + 4 KOH + 2 I_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 2 | -2 SO_2 | 1 | -1 KI | 4 | -4 S | 1 | 1 KOH | 4 | 4 I_2 | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) KI | 4 | -4 | -1/4 (Δ[KI])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) I_2 | 2 | 2 | 1/2 (Δ[I2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/2 (Δ[H2O])/(Δt) = -(Δ[SO2])/(Δt) = -1/4 (Δ[KI])/(Δt) = (Δ[S])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/2 (Δ[I2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | potassium iodide | mixed sulfur | potassium hydroxide | iodine formula | H_2O | SO_2 | KI | S | KOH | I_2 Hill formula | H_2O | O_2S | IK | S | HKO | I_2 name | water | sulfur dioxide | potassium iodide | mixed sulfur | potassium hydroxide | iodine IUPAC name | water | sulfur dioxide | potassium iodide | sulfur | potassium hydroxide | molecular iodine